Combine the warm water and sugar, sprinkle the active dry yeast over the top and let sit briefly until foamy. Add the flour, salt, and two tablespoons of softened butter, then knead until the dough becomes smooth and elastic. This can take 8–10 minutes by hand or 5–7 minutes in a stand mixer with a dough hook. Place the dough in a lightly oiled bowl, cover, and let it rise until doubled in size in a warm spot.

Pro Tip: The dough should be tacky but not sticky and pass the windowpane test.

Melt the remaining two tablespoons of butter in a small pan over medium-low heat, add the minced garlic and cook very briefly until fragrant—do not brown. Stir in the chopped thyme and remove from heat, then let the herb butter cool to room temperature.

Pro Tip: The butter should smell bright and herbal with a gentle garlic perfume.

Punch down the risen dough and roll it into a large rectangle on a lightly floured surface. Brush the entire surface with the cooled herb butter, then sprinkle an even layer of shredded mozzarella over the butter.

Pro Tip: The rectangle should be roughly even thickness.

Roll the rectangle tightly into a log, seam-side down. Slice the log lengthwise into two equal strands and twist the two strands together. Transfer to a greased loaf pan and cover.

Pro Tip: The twist should look like two rope strands.

Brush the risen loaf with the beaten egg for a glossy finish. Bake in a preheated oven at 350°F for about 30 minutes until the crust is deep golden brown.

Pro Tip: The crust should be evenly golden and sound hollow when tapped.